No, they're different. White balance is the ratio of r/g/b necessary to make the colors accurate - because different sources of light make different colors of white. For example, tungsten light bulbs are yellower than sunlight, and on cloudy days it's bluer than normal. Setting the white balance makes the whites white which in turn corrects the rest of the colors.
Color space is a set of colors designed to model the capabilities of a particular output or input device. sRGB models the range of colors that a standard monitor can produce, which is rather limited. AdobeRGB, on the other hand, has a broader range of colors that is better matched to high-quality printers. If you're mainly taking pictures for the web, use SRGB. If you plan on making fine adjustments to your images for high-quality output, use AdobeRGB.
For a better explanation of color space, go to this link.http://www.drycreekphoto.com/Learn/color_spaces.htm